An infinite number of effectively infinite clusters in critical percolation

Naeem Jan; Dietrich Stauffer; Amnon Aharony

doi:10.1023/a:1023008021962

An infinite number of effectively infinite clusters in critical percolation

Naeem Jan, Dietrich Stauffer, Amnon Aharony

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

An infinite number of effectively infinite clusters are predicted at the percolation threshold, if "effectively infinite" means that a cluster's mass increases with a positive power of the lattice size L. All these cluster masses increase as L^D with the fractal dimension D = d - β/v, while the mass of the rth largest cluster for fixed L decreases as l/r^λ, with λ = D/d in d dimensions. These predictions are confirmed by computer simulations for the square lattice, where D = 91/48 and λ = 91/96.

Original language	English
Pages (from-to)	325-330
Number of pages	6
Journal	Journal of Statistical Physics
Volume	92
Issue number	1-2
DOIs	https://doi.org/10.1023/a:1023008021962
State	Published - 1 Jan 1998
Externally published	Yes

Keywords

Infinite clusters
Percolation
Ranking
Size distribution

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1023/a:1023008021962

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AU - Jan, Naeem

AU - Stauffer, Dietrich

AU - Aharony, Amnon

PY - 1998/1/1

Y1 - 1998/1/1

N2 - An infinite number of effectively infinite clusters are predicted at the percolation threshold, if "effectively infinite" means that a cluster's mass increases with a positive power of the lattice size L. All these cluster masses increase as LD with the fractal dimension D = d - β/v, while the mass of the rth largest cluster for fixed L decreases as l/rλ, with λ = D/d in d dimensions. These predictions are confirmed by computer simulations for the square lattice, where D = 91/48 and λ = 91/96.

AB - An infinite number of effectively infinite clusters are predicted at the percolation threshold, if "effectively infinite" means that a cluster's mass increases with a positive power of the lattice size L. All these cluster masses increase as LD with the fractal dimension D = d - β/v, while the mass of the rth largest cluster for fixed L decreases as l/rλ, with λ = D/d in d dimensions. These predictions are confirmed by computer simulations for the square lattice, where D = 91/48 and λ = 91/96.

KW - Infinite clusters

KW - Percolation

KW - Ranking

KW - Size distribution

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An infinite number of effectively infinite clusters in critical percolation

Abstract

Keywords

ASJC Scopus subject areas

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